P$_ell$-Kyber: Packing $ell$ Plaintexts and Lattice Coding for Kyber

2025-04-24

AI Summary

Lattice-based KEMs such as Kyber suffer from high decryption failure rates (DFR), large communication overhead, and traditional security analyses that critically rely on the unrealistic independence assumption of decryption noise. Method: This paper proposes a unified ciphertext packing and lattice packing framework. It introduces the first multi-level plaintext packing combined with cross-layer lattice encoding for Kyber, eliminating dependence on noise independence. A rigorous security proof is established via M-LWE reduction, extending the PVW framework to support $ell$-dimensional plaintext packing and incorporating high-dimensional lattices—e.g., the Leech lattice—for efficient joint encoding. Results: For the $ell = 24$, KYBER1024 instantiation, the DFR is reduced to $2^{-281}$ and communication overhead drops to 4.6, achieving a 90% reduction compared to the baseline.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Security and Privacy: Applications of cryptography
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

In this work, we propose a joint design of encoding and encryption processes for KEMs like Kyber, without assuming the independence of the decoding noise entries. Our design features two techniques: ciphertext packing and lattice packing. First, we extend the Peikert-Vaikuntanathan-Waters (PVW) method to the Kyber: $ell$ plaintexts are packed into a single ciphertext. This scheme is referred to as P$_ell$-Kyber. We prove that the P$_ell$-Kyber is IND-CCA secure under the M-LWE hardness assumption. We show that the decryption decoding noise entries across the $ell$ plaintexts (also known as layers) are mutually independent. Second, we propose a cross-layer lattice encoding scheme for the P$_ell$-Kyber, where every $ell$ cross-layer information symbols are encoded to a lattice point. This way we obtain a emph{coded} P$_ell$-Kyber, where the decoding noise entries for each lattice point are mutually independent. Therefore, the decryption failure rate (DFR) analysis does not require the assumption of independence among the decryption decoding noise entries. Both DFR and communication cost (CER) are greatly decreased thanks to ciphertext packing and lattice packing. Finally, we demonstrate that with $ell=24$ and Leech lattice encoder, the proposed coded P$_ell$-KYBER1024 achieves DFR $<2^{-281}$ and CER $ = 4.6$, i.e., a decrease of CER by $90%$ compared to KYBER1024.

Problem

• Enhance Kyber KEM with joint encoding and encryption design
• Achieve IND-CCA security under M-LWE assumption for P$_ell$-Kyber
• Reduce DFR and CER via ciphertext and lattice packing

Innovation

• Extends PVW method to Kyber for ciphertext packing
• Proposes cross-layer lattice encoding for noise independence
• Achieves lower DFR and CER via packing techniques